Syntactic type abstraction

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Abstract
Software developers often structure programs in such a way that different pieces of code constitute distinct principals . Types help define the protocol by which these principals interact. In particular, abstract types allow a principal to make strong assumptions about how well-typed clients use the facilities that it provides. We show how the notions of principals and type abstraction can be formalized within a language. Different principals can know the implementation of different abstract types. We use additional syntax to track the flow of values with abstract types during the evaluation of a program and demonstrate how this framework supports syntactic proofs (in the sytle of subject reduction) for type-abstraction properties. Such properties have traditionally required semantic arguments; using syntax aboids the need to build a model and recursive typesfor the language. We present various typed lambda calculi with principals, including versions that have mutable state and recursive types.

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